where \(\mathbb {B}(\epsilon ) = \lbrace x^{\prime }\in \mathbb {R}^d: ||x^{\prime } - x||\le \epsilon \rbrace \)  is the set of samples perturbed around \(x\)  with \(l_\infty \)  distance \(\le \epsilon \) .
Yin et al. [1]} prove that the lower bound for the Rademacher complexity of \(\mathcal {F}\)  is \(\Omega (||X||_F/n + \epsilon \sqrt{d/n})\) . This lower bound exhibits an explicit dependence on the input dimension \(d\) .
